Fully broken iphone screen - doesn't switch on

A few days ago my phone fell face first from my table onto the floor. When I picked it up, I noticed the screen guard was fully broken and only the part of the screen was visible (below where the time is shown). The next morning, the screen seemed to be fully broken as it was not switching on at all, I tried multiple times but the screen didn't switch on. I connected it to my PC and itunes recognized it as a working iphone. I tried backing it up but it asked me to enter the passcode on my iphone screen (something I cannot do as the screen isn't switching on) can someone tell me what to do from here?

Is my iphone fully broken or is it just the broken screen? can the screen be fixed at an apple service centre? How do I back it up to itunes without entering the passcode? If it is just a broken screen i'll have to wait a few months after lockdown in my country ends before going to get if fixed. I have no warranty.

It's a Space grey iphone 6s 32gb which I purchased new from Amazon in April 2018. This is not a used phone.